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Updated: Jun 18, 2026
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard
Charles H Bennett1, Debbie Leung, Graeme Smith
1IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA. bennetc@watson.ibm.com
Physical Review Letters
|November 13, 2009
Summary
Closed timelike curves (CTCs) do not aid in distinguishing nonorthogonal quantum states or speeding up computations when inputs are mixtures. Nonlinear quantum mechanics with CTCs offers no advantage in these scenarios.
Area of Science:
- Quantum Mechanics
- Theoretical Physics
- Computational Complexity
Background:
- Nonorthogonal quantum states present challenges in quantum information processing.
- Closed timelike curves (CTCs) and nonlinear quantum mechanics are theoretical constructs with potential computational applications.
- Previous claims suggested CTCs could enhance quantum computation capabilities.
Purpose of the Study:
- To investigate the utility of closed timelike curves (CTCs) and nonlinear quantum mechanics for distinguishing nonorthogonal states.
- To evaluate the potential of CTCs and nonlinear evolution in accelerating complex computations.
- To resolve discrepancies with prior research on CTC-assisted computation.
Main Methods:
- Analysis of CTC-assisted quantum computer models.
- Examination of quantum state distinguishability with mixed inputs.
- Definition and evaluation of computational tasks under nonlinear evolution.
Main Results:
- CTCs provide no advantage for distinguishing nonorthogonal states when presented as labeled mixtures.
- Nonlinear evolution in CTC-assisted systems does not yield a convex combination of outputs for mixed inputs.
- The efficacy of CTCs and nonlinear evolution for accelerating hard computations remains unproven under standard computational definitions.
Conclusions:
- The practical advantage of CTCs for distinguishing quantum states or speeding up computations is limited, particularly with mixed inputs.
- Nonlinearity introduced by CTCs complicates direct application of standard quantum computing paradigms.
- Further research is needed to clarify the precise role and limitations of CTCs in quantum computation.
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